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Search: id:A001636
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| A001636 |
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A Fielder sequence: a(n)=a(n-1)+a(n-2)-a(n-7), n>=8.
(Formerly M0763 N0290)
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+0
1
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| 0, 2, 3, 6, 10, 17, 21, 38, 57, 92, 143, 225, 351, 555, 868, 1366, 2142, 3365, 5282, 8296, 13023, 20451, 32108, 50417, 79160, 124295, 195159, 306431, 481139, 755462, 1186184, 1862486, 2924375, 4591702, 7209646, 11320209, 17774393, 27908418
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: x^2*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7).
a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6), n>=7.
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MAPLE
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A001636:=-z*(2+3*z+4*z**2+5*z**3+6*z**4)/(z+1)/(z**5+z**3+z-1); [S. Plouffe in his 1992 dissertation.]
(Maple) a := n -> (Matrix([[6, -1$4, 4, 5]]). Matrix(7, (i, j)-> if (i=j-1) then 1 elif j=1 then [1$2, 0$4, -1][i] else 0 fi)^n)[1, 1] ; seq (a(n), n=1..38); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(x^2*(2+x+x^2+x^3+x^4-6*x^5)/(1-x-x^2+x^7)+x*O(x^n), n))
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CROSSREFS
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Cf. A013983.
Sequence in context: A066895 A105075 A140669 this_sequence A036588 A099517 A026647
Adjacent sequences: A001633 A001634 A001635 this_sequence A001637 A001638 A001639
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Michael Somos, Feb 17, 2002
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